Iterative schemes for solving sparse linear systems arising from elliptic PDEs are very suitable for efficient implementation on large scale multiprocessors. However, these methods rely heavily on effective preconditioners which must also be amenable to parallelization. In this paper, we present a novel method to obtain a preconditioned linear system which is solved using an iterative method. Each iteration comprises of a matrix-vector product with k sparse matrices (k logn), and can be computed in O(n) opertions where n is the number of unknowns. The numerical convergence properties of our preconditioner are superior to the commonly used incomplete factorization preconditioners. Moreover, unlike the incomplete factorization preconditioners, our algorithm affords a higher degree of concurrency and doesn't require triangular system solves, thereby achieving the dual objective of good preconditioning and efficient parallel implementation. We describe our scheme for certain linear systems with symmetric positive definite or symmetric indefinite matrices and present an efficient parallel implementation along with an analysis of the parallel complexity. Results of the parallel implimentation of our algorithm will also be presented in the final version of this paper.
求解椭圆形PDE引起的稀疏线性系统的迭代方案非常适合在大型多处理器上高效实现。但是,这些方法严重依赖于有效的预处理器,这些预处理器还必须适用于并行化。在本文中,我们提出了一种获取预处理线性系统的新方法,该方法可以使用迭代方法求解。每次迭代均包含具有k个稀疏矩阵(k
机译:具有可变系数的三维椭圆PDE的并联循环减少预处理器
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机译:一类椭圆PDE系统的并行代数多层Schwarz预处理器
机译:椭圆形PDE的并行预处理器
机译:扩散图及其在时间序列预测和过滤和二阶椭圆PDE的应用
机译:椭圆形偏微分方程系数的生物组织有效吸收率
机译:变系数三维椭圆PDE的并行加速循环归约预处理器